Hydrogenated block copolymers are highly valued for applications in films/fibers or molded articles by way of forming processes such as injection molding, blow molding, film extrusion, fiber extrusion, film blowing and others. Hydrogenated block copolymers have the advantage of allowing complete recyclability of scrap and used articles. The applications come from a variety of polymer compositions containing hydrogenated block copolymer and other materials. Unfortunately, the conventional polymer compositions often are difficult to be processed due to the significant difference of the rheology and tensile properties in different orientations. This results in highly oriented articles which may warp or exhibit properties difficult to predict. It also makes the injection molding of thin walled parts, films and fibers difficult or impossible. Prior art documents, for example, U.S. Pat. No. 5,705,556, U.S. Pat. No. 6,310,138, U.S. Pat. No. 7,439,301, US 2011/0262686, U.S. Pat. No. 7,268,184, etc., mainly disclose such conventional polymer compositions, which all lack the study of required rheology and tensile properties, and thus fail to provide solutions for the high orientation problems. Therefore, there is a need for providing a polymer composition containing hydrogenated block copolymer and having good performance characteristics to solve the problems in the prior art.